Science:Math Exam Resources/Courses/MATH152/April 2010/Question B 05 (b)/Solution 1

From UBC Wiki

Continuing from the hint, to choose real-valued solutions, we choose , so that the general solution becomes:

Recall that


The general form of real-valued solutions is:

where and are real constants.

Their relationship with the previous constants are and

Now if we impose the initial condition , we get

Thus, and , and the solution of the initial value problem is

Alternatively, one can solve directly from

And impose the initial condition direcly to find that .

Then compute the real part to get the same result as above. The amount of algebra involved will be slightly less.